[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{vertex}{(\stackrel{h}{2}~~,~~\stackrel{k}{-3})}\qquad y=a(x-2)^2-3~\hfill \textit{we also know that} \begin{cases} x=0\\ y=5 \end{cases} \\\\\\ 5=a(0-2)^2-3\implies 5=4a-3\implies 8=4a\implies \cfrac{8}{4}=a\implies 2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=2(x-2)^2-3~\hfill[/tex]
